Active_Crossovers_and_Filters

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What are active crossovers? In short, theyelectronic circuits that divide the audio spectrum

up into discrete bands of frequencies and theyfunction in place the passive crossovers found in

loudspeakers. The underlying motivation for theswitch to an active crossover is the improved

accuracy and flexibility of the active crossover

holds over the passive crossover.Loudspeakers represent truly complex

impedances, which only an equally complexpassive crossovers can match. Thus deriving the

required crossover frequency and slope isdifficult with a passive crossover and changing a preexisting passive crossover frequency is

anything but easy. Active crossovers, on the

other hand, remove the large passivecomponents that make up the passive crossover.

This is for the good, as the hundred feet ofmagnet wire that makes up the inductors and the

two back-to-back electrolytic capacitors thatmake up most crossover non-polarized

capacitors are not missed: these components are

far from ideal. And the power amplifier, oncefreed from having to work through this dreck,exercises a better control of the loudspeaker

drivers. For example, a damping factor of 100

means little, if the passive crossover adds 1 ohmof DC resistance to the mix, thereby decreasing

the effective damping ratio to 8.Active crossovers also allow for a frequency

tailoring that would be altogether impossible orat least incur efficiency penalties with a passive

crossover. For example, with a network

designed by Linkwitz, we can effectively shiftthe resonant frequency and Q of a loudspeakerdriver. Furthermore, a high Q crossover can

boost a drooping low frequency response of alow Q speaker while filtering away sub-sonic

garbage, such as record warp.

Bi-Ampping Psycho-AcousticsAn added advantage is a psycho-acoustic

phenomena wherein bi-ampped systems seem

more powerful than the sum of the amplifier

wattages, e.g. two 36 watt amplifiers soundmuch more powerful than a 72 watt amplifier.

How is that possible? Half of the answer lies

in the output voltage adding together rather thanthe wattages adding together. Wattage is basedon the voltage squared. For example, 24 peak

volts of output signal equals 36 RMS watts, but48 peak volts of output signal equals 144 RMS

watts. In other words, doubling the voltagequadruples the wattage; tripling, increases the

wattage by ninefold.

Active Crossovers and Filters

Let's imagine a crossover point of 500 Hz. If a

144 watt amplifier is presented with a signal oftwo 24 volt tones, say 100 Hz and 2 kHz, the

signal will trace a 2 kHz sine wavesuperimposed on a 100 Hz wave. The total peak

voltage is 48 volts, which equals 144 RMSwatts. Remember that a given instant the

amplifiers output is at only one specific voltage.(The plate cannot be at +24 and at 12 volts at

the same time. We are dealing with cooper wireand voltage, not fiber optics and light.) A

passive crossover splits these two frequencies

from the output from a 144 watt amplifier intotwo 24 volt signals. The active crossover alsoseparates the two frequencies so that two 36 watt

amplifiers can play these two tones at the samevolume as the single 144 watt amplifier can, i.e.

24 volts at 100 Hz and 24 volts at 2 kHz.

2 kHz200 Hz20 Hz 20 kHz

+ =200 Hz

2 kHz

200 Hz + 2 kHz added together


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Of course, if both tones had been at

frequencies below the 500 Hz crossover point,say 100 and 300 Hz, one 36 watt amplifier

would clip its output while the second amplifiersat idle. While this seems to limit the power

increasing effect, this indirectly leads to secondpower increasing effect.

One last argument in favor of active

crossovers: headphone listening can be superb, but it suffers from the lack of a visceral

component; the floor just doesnt shake withheadphonesbut it can. For over two decades

my preferred way of listening to headphones has been to use them with powered subwoofers.

With a high frequency limit of 80 Hz thesubwoofers seldom even move with pop music,

but with Mahlers 3rd symphony, they workovertime. (The missing octave is filled in and yet

your neighbors have a hard time locating you as

the source of the low growls, as the ear has ahard time localizing ultra-low frequencies.)

Filter TypesWhat is the difference between a crossover

and filter? A crossover is specifically meant to

work with loudspeakers and it is usually madeup of several filters. In other words, a filter is the

more general term, which suits a circuit that hassuch a wide application. Almost all electronic

devices employ some filters. The radio and TV

set are filters of sorts, as they select only anarrow band of frequencies at a time. A filter

can be made out of as little a single capacitor orinductor (and a load resistance). A filter can also

consist of twenty resistors and twenty capacitorsand many amplifiers.

FiltersAnalog Digital

Passive Active

Lowpass Lowpass

Bandpass Bandpass

Notch Notch

Highpass Highpass

+ =100 Hz

300 Hz

The ear is most sensitive at about 3 kHz

(roughly, the resonate frequency of the earcanal). As the frequency falls from this

frequency, so does our sensitivity to it. So if a bi-ampped system sees a signal that only clips

the woofer amplifier, the ear will not complainas much as it would if the tweeter amplifier had

clipped. A further reason is that woofers areslow heavy devices that cannot reproduce the

harsh high harmonic of the clipped lowfrequency waveform. So while a low frequency

amplifier may clip repeatedly, the woofer willnot readily betray that fact. And since it isusually the low frequencies the demand the

greatest share of power, the two 36 wattamplifiers may even seem more powerful than a

144 watt amplifier as long as the high frequencyamplifier has not clipped. (This might helpexplain why a 3 watt tube SE amplifier can

sound as powerful as a 30 watt solid-state

amplifier: the ear hears clipping as the limit to power. Transformer coupled, feedback free

amplifiers have the softest clippingcharacteristics of any amplifier, as thetransformers limit the transfer of highfrequencies and the absence of feedback means

the driver stage will not try force a sharper slopeon the output tubes flattened waveform.)

100 Hz + 300 Hz added together and clipped

In all filters, however, some frequencies are

allowed to pass, while others are attenuated. The portion that is allowed to pass is named the passband and the portion that is excluded is

named the stopband and the portion of overlap between these two bands is named the

transitional-band.


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If only low frequencies are passed, we call this

filter a low-pass filter, as that is what it passes. If

only high frequencies are passed, we call thisfilter a high-pass filter. If only a band of

frequencies, say 500 to 5000 Hz, are passed, wecall this filter a band-pass filter. If all frequency

are passed save for a very narrow band offrequencies, we call this filter a notch filter.

Beyond these four basic divisions, a furtherclassification is applied based the steepness ofthe rejection of undesired frequencies.

Since the slopes steepness is marked by the

order in a filters design. (The number of poles

is also sometimes used as a short handdescription of the steepness.) For example, a

single order filter, also called a single pole filter,has a crossover slope of -20 dB per decade,which equals -6 dB per octave. Thus a second

order filter attenuates at 12 dB per octave; athird order filter, -18 dB per octave; a fourth

order filter, -24 dB per octave; a fifth orderfilter, -30 dB per octave; and a sixth order

filter, -36 dB per octave.

The most common filter alignments are the

Butterworth and the Bessel (AKA Thomson).Less common alignments are the Gaussian,

Chebyshev and the elliptic (AKA Cauer). Arecent addition to the palette of filters is the

Linkwitz-Riley alignment (AKA Butterworthsquared), which was specifically designed for

use as loudspeakers crossover (More on this typeof filter to follow.).

Common Audio Filter TypesThe Butterworth filter is the most commonly

used filter type in audio applications. It has afairly flat time response, a fairly crisp transition

shape and the flattest passband response. Incontrast, the Bessel filter offers a flatter time

response, but not as sharp a transition shape orflat a passband response. The Chebyshev and the

elliptic filter are seldom used in everyday audiogear, as these filters bring too many undesirable

characteristics such as ripples in the passband orwild phase shifts.

The Linkwitz-Riley filter improves on the

Butterworth when feeding loudspeakers. Oddorder crossovers (6 dB and 18 dB per octave

filters) are marked by of 90 degree multiples in phase differences between outputs. The sum of

two 90 degree equal amplitude signals is +3 dB boost in output. Thus the 3 dB point of the

filter works to yield a flat transition region.Even-order crossovers (12 dB and 24 dB per

octave filters) are marked by 180 degreemultiples of phase differences between outputs.

The sum of two 180 degree phase shifted, butequal amplitude, signals is a deep null in the

output. The solution is to reverse the phase ofone of the loudspeaker drivers to eliminate the

phase difference at the crossover frequency.However, when two loudspeakers play the exact

same signal (no amplitude or phase differences),

the result is a twofold increase (+6 dB boost) involume. So if we wish to reconstruct the outputsof one lowpass and one highpass filter, we must

tailor the attenuation at the crossover frequency

to match the intended summing device.

Lowpass Bandpass HighpassNotch

F 10F0

-20

-3

1st2nd3rd4th

The next taxonomic division is made based onthe filters alignment. The alignment is based on

the relative position of the poles in the filter,which in turn gives rise to the different shapes

each filter exhibits across its frequency range.

Some filters offer a sharp transition from passband to stopband, but at the cost of some

ripple and even ringing in the frequencyresponse. Other filters offer a soft transition that

droops at the transition frequency that is ripplefree. In short, an analog filters design hopes to

optimize one or two parameters, but always atthe cost of some other parameters.


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Thus, when using loudspeakers that see the

same phase and amplitude signal, we cannot usea 3 dB down point, as it would yield +3 dB;

thus, we need a 6 dB attenuation at thecrossover frequency in order to ensure a flat

frequency response. The same phase is the keypoint here. If a Butterworth second or fourth or

sixth order crossover is used, the frequencyresponse will display a bump at the crossover

frequency. On the other hand, using a Linkwitz-Riley 2nd or fourth order crossover will yield a

flat frequency response at the crossover

frequency.Well at least that is the theory. Complications

arise: the distance between drivers, thefrequency response of each driver, the front-to- back spacing of the drivers voicecoils. If the

distance between drivers exceeds the wavelength

of the crossover frequency, or if one or bothdrivers droop at the crossover frequency, or if

the tweeter acoustic center is substantially infront of the woofers, then the Butterworth

aligned crossover might actually prove flatter.Do not falsely imagine that an even order

crossover is phase flat; it isnt. The actual phaserelation between 2nd order lowpass and

highpass filters is a constant 180 degrees phasedifference, which when one driver's connection

is inverted, yields a constant phase relation

between drivers, but not a flat phase response.

A Phase Flat LoudspeakerOne interesting loudspeaker configuration

was created by Philips. An ostensibly two-wayloudspeaker was designed using a second order

Butterworth crossover, but without the tweetersphase reversal. Yes this resulted in a deep suck-

out. The suck-out was then filled in by using a bandpass filter (-6 dB slopes) feeding a full-

range driver. This extra speaker saw only the

crossover frequency unattenuated, as all thefrequencies below or above this frequency were

attenuated at 6 dB per octave. The sum of allthree drivers output equaled a phase-coherent

flat frequency response. In this speaker system,the woofer was prevented from going too high,

while the tweeter is protected from lowfrequencies, while fullrange driver filled in the

hole. Unfortunately, this solution, like mostspeaker innovations, disappeared long ago.

0-3

Crossover Testing

Evaluating active crossovers under actual use

is difficult. Which component is making thebiggest difference? The active crossover itself or

the extra amplifiers and speaker cables? Alistening test I have used is to take a pair of

fullrange conventional loudspeakers and applythe crossover under test using my present

amplifier and cables. This means there is noworry about relative efficiencies and frequency

response limitations.

The procedure is simple enough; place onespeaker on top of the other and set the crossover

frequency to some value between 300-700 Hz(too high a frequency will result in lobbingeffects due to greater than wavelength spacing

between drivers). This test requires a monosignal source and I recommend any of the mono

Verve recordings of Ella Fitzgerald.

Phase differences between 2nd order Butterworthhigh-pass filter (white line) and its low-passcomplement (yellow line)

Fc/10 Fc 10xFc

180

0

-180


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General crossover test setup

500 Hz

500 Hz

First listen to just the loudspeaker on top

(fullrange, without the active crossover in otherwords). It takes some time to get used to mono,

so play about 30 minutes worth. Next introduce

the active crossover and feed the highpass signalto the top loudspeaker. Now listen to the same

30 minutes of music.

Loudspeaker diaphragms move in response to

signals and the large diaphragm movements

caused by low frequencies raise the highfrequencies while the drivers cone movestoward us and then lower the high frequencieswhen the cone moves away from us.

Consequently, in absolute terms, it is impossiblefor anyone driver to reproduce more than one

pure tone at a time. This is one reason why

electrostatic and planer speakers sound as goodas they do; the large surface areas do not need to

move very far to produce high sound levels.Three-way, four-way, five-way, and six-way

loudspeaker also greatly reduce this distortion,while admittedly adding huge crossover

problems. And the worst offenders are smallfullrange single driver based loudspeakers.

Bi-Ampped Identical LoudspeakersI once heard something like the test setup with

four large Advent loudspeaker from the early80s. A friend bought four speakers for

quadraphonic use and instead used all four in astereophonic setup with a active crossover set at

100 Hz. The improvement in midrange clarityand bass definition was markedly better. In fact,

it sounded much better than it should seempossible. (A similar experience occurred when I

heard a speaker setup that consisted of eight highquality mini-monitors configured as two

speakers. No crossover was used and fourspeaker enclosures were stacked on each other

per side, with only one facing the listener. The

resulting impedance was identical to that of asingle speaker, as they were wired in series-

parallel. Because each speaker saw half of theavailable output voltage from the power

amplifier, its response was down 6 dB; but as theradiating area had increased fourfold, the output

response gained +12 dB of gain, which in theend, yielded +6 dB of gain.)

If the crossover is working well, the soundshould be very similar to that from the single

loudspeaker. The usual result is that the sound ismuch better than that from the sole speaker.

Why? The power increasing effect is part of thereason. The rest of the answer is found in the

reduction in distortion that results from freeingthe top loudspeaker from the onerous task of

reproducing low frequencies. In other words,

the top loudspeaker is less likely to mechanicallyclip. Furthermore, there is a large reduction in aseldom mentioned distortion: frequency

modulation distortion, FMD.

FMDThis distortion is related to Doppler

distortion: the phenomenon of frequencies

increasing in pitch as a sound producing objectnears us and the sound decreasing in pitch as the

object retreats. The sound of a race car

approaching and passing is the usually givenexample. RRRRR R R R R R R R R R R.


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+

-

+

+

In same vein, if you are pleased with your

present loudspeakers, but wish that they provided a little more headroom or clarity at

high volumes, then this doubling ofloudspeakers might be the best way to go.

Active crossovers are certainly nice, but notstrictly necessary, as one choke and one

capacitor are all that is needed to make a passivesingle order crossover. My recommendation is to

select a crossover frequency that is thegeometric mean of the lowest and highest

frequencies produced by your loudspeakers. For

example, 600 Hz for speakers that extend downto 20 Hz and up to 20 kHz; 1400 Hz for that

only extend down to 100 Hz (mini-monitors).

Fgeometric = (Flow x Fhigh)I also recommend using the shunt arrangement

rather than the series, as it provides better

damping. (The shunt arrangement attenuates thestopband by shunting the driver with an everdecreasing impedance; where the series

arrangement attenuates the stopband by presenting the driver with an ever increasing

impedance.) Of course, with a passive crossover,none of the power increasing effects are

bestowed.

Choosing Crossover SlopesIn theory, nothing beats a simple 1st order

crossover. It results in a flat, time coherentfrequency response. Actual practice differs. The1st order filter provides a shallow attenuation

slope that is too gradual to protect fragile

tweeters from brutal low frequencies and toogradual to keep woofers from working up into

1st 3rd

100 Hz

their high frequency limits, as a two to three

octave overlap is recommended to make thisfilter work well. However, as the number of

crossover points increase, the more likely it isthat this gentle filter slope will provide sufficient

protection.On the other hand, if you are adding a powered

subwoofer to an existing fullrange loudspeaker,the 1st order highpass filter is a good choice for

the fullrange speaker and a 3rd order filter forthe subwoofer. This combination seems to work

well in terms of amplitude response. It also has a

minimalist aspect that is gratifying: thesubwoofer contributes only its low frequency

heft and then quickly gets out of the way of thelower midrange; the satellite loudspeaker sees avery gentle highpass slope that allows it extend

down into the deep bass as it very slowly falls

off in volume with decrease frequency.

Those using zero feedback tube amplifiers,

will find a preexisting 1st order highpass filter in

their power amplifiers. The coupling capacitorthat connects to the grids of the output tubesdefines a highpass filter that is usually set tosome very low frequency, such as 1 to 5 Hz.

Decreasing the value of this capacitor raises thecrossover frequency. By choosing the right

value, we can forgo the need for an external

crossover. The formula is an easy one:

C = 159155/Fc/R,

Where Fc equals the desired crossoverfrequency, C equals the value of the coupling

capacitor in F, and R equals the value of thegrid resistor. Truly minimalist. One trick I have

wanted to try for some time now is using asatellite loudspeaker (a sealed box with a Q of 1)

along with a 1st order filter, which comes with aQ of 0.707 (set to the Fo of the enclosure).


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The Qs are multiplied against each other,

which will give the loudspeaker an effective Qof 0.707. The advantage of this arrangement lies

in the smaller enclosure needed for a higher Qloudspeaker alignment and the natural 2nd order

highpass filter function of the sealed boxenclosure adding to 1st order filter to make a 3rd

order highpass filter with a -3 dip at thecrossover frequency.

To work best this 1st order filter must comebefore the power amplifier, as using a capacitor

in series with the loudspeaker will not work due

to the impedance spike at the speakersresonance. The subwoofer's lowpass filter should

be actively realized with an active 3rd orderButterworth filter. A further refinement would be to add an active 2nd order or 4th order

highpass filter whose cutoff frequency would

equal the Fs of the subwoofer. This would bothwork to protect the satellite speaker from

excessive low frequency cone excursions andwork to bring both subwoofer and satellite into

the same phase relationships, as the subwoofersown box resonance defines a highpass filter (2nd

order for sealed boxes and 4th order for bass-reflex enclosures.)

1st 3rd

100 Hz

2nd

30 Hz

3rd

For most drivers that suffer from either

limited power handling or limited frequencyresponse, sharper cutoffs are needed. The 2nd,

3rd, and 4th order slopes both protect and isolatethe drivers. Many audiophiles, however, distrust

higher order filters, fearing the signals phasereversals and complexity of the crossovers. Yet

they do not realize that the speakers themselves bring phase aberrations because of resonancesdriver breakup at higher frequencies. For

example, most tweeters have a resonantfrequency between 800 to 2 kHz and all cone

and dome drivers must flex once thecircumference of the diaphragm becomes largerthan the twice the wavelength of the frequency

being reproduced. (Strictly speaking, for

example, we should not let an 8 inch wooferextend beyond 1400 Hz; but we do so regularly.)

Here is where active filters shine. As has beenmentioned, the problem with using passivefilters with loudspeakers is that they seldomfunction entirely to plan and this poor

performance is due to the passive componentsfalling short of their ideals.

Inductors (chokes) are made up of longlengths of wire, which adds resistance. Capacitor

also carry an ESR (effective series resistance)

that upsets inter-relations within the filter. Andloudspeaker drivers are anything but pure

resistances. All of these failings add up to a filterthat does not match its textbook model. On the

other hand, the active filter can match itstextbook template easily. Additionally, active

filters can make do with only resistors andcapacitors to define their poles. Doing without

inductors is a relief in terms of money and space,as the lower the frequency, the bigger the

inductor. And because the active filter presents

an almost infinite input impedance to thefrequency tailoring parts, high valued resistors

can be used, which only require small valuedcapacitors to match. For example, an 8 ohm

loudspeaker driver crossing over at 1 kHzrequires a 20 F capacitor, whereas a 10k

resistor only needs a .0159 F capacitor. In otherwords, active filters present a win, win situation.

Using the speaker's own effective filters to completea crossover . Here the speaker's 2nd order functionis added to a 1st order filter to yield an effective 3rdorder slope.


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Mix and MatchActive filters can be cascaded to yield a

degree of frequency tailoring that is all butimpossible with passive filters. The passive filter

works best with known, fixed input andterminating impedances, which a cascading

passive filter cannot readily do.For example, two active 3rd order filters

cascaded equals a 6th order filter. An active

highpass and a lowpass filter cascaded can yieldbandpass filter; and these same filters fed into a

mixer can yield a notch filter.

ConclusionIn this article we have looked into the why

bother with active crossovers and filters? Wehave seen that active crossovers and active

filters in general offer some real advantages over

their passive brethren, as they are more accurate,flexible, and easy to implement. In the nextarticle, we will look into designing tube

crossovers.

//JRB

Suggested Readings

Active Filter Cookbook

By Don Lancaster, 1975, 95, 96

IC based active filters explained in detail. A

classic that is readily available new and used.

Audio/Radio Handbook

By National Semiconductor, 1980

This book has a chapter whimsically namedFloobydust, which covers some interesting

active crossovers, including asymmetrical filters.

Passive and Active Filters

By Wai-Kai Chen, 1986

The book to own, if you are serious about filters.

A classic, but not for those fearful of math.

Understanding Electronic Filters

By Owen Bishop, 1996This book is the best place for the novice to

start. Should be read from start to finish.

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